The Force and Failure of Parmenides' Argument

As we said yesterday, the central Thesis (CT) of Parmenides' argument is that "that which does not exist cannot be thought or spoken about." The argument depended on two premises:

1) A thing can be thought about only if it is possible for it to exist.

2) Anything that does not exist, cannot exist.

The contraposition of (2), led to (3) [see yesterday's post for premises 3-5]; then the hypothetical syllogism of (1) and (3) led to (4). Finally the contraposition of (4) led to (5, which is the central thesis.

The result of our analysis was that given the truth of (1) and (2), the argument did follow through to the central thesis. The question, then, is whether (1) and/or (2) is true or false. We examined (1) and found that to be most likely true. (2) however was not so lucky. There seems to have been an equivocation (change of meaning) on Parmenides' part regarding existence. It is not clear whether he meant a possible type of existence or an actual type of existence. (Clearly he would have not thought in these terms, but we can worry about his argument in this way.) If in (3) he means something like "possible existence", then the proposition becomes redundant, since the latter part of the proposition is already about possible existence. So it must be that he meant something like "Anything that does not actually exist, cannot exist." This, proposition, however, seems false, since it is true that my third child does not exist, but it is not true that it cannot exist. The counterexample shows that premise (2) is most likely false, and that the argument of Parmenides for the central thesis fails.

Since the argument that we considered depended on the correct definition of "existence", it is essential that we begin our philosophy with philosophical definitions, much like the ones that Socrates asks for in Plato's dialogues. We thus now move on to the Euthyphro

The Argument of Parmenides

Just for fun, see if you can recreate the way we wrote the argument out in class. (Much of the work comes from M. Cohen's work on the history of Ancient philosophy):

1) A thing can be thought about only if it is possible for it to exist.

2) Anything that does not exist, cannot exist.

But 2 is equivalent by contraposition to:

3) Anything that can exist, does exist.

From (1) and (3) it follows that:

4) A thing can be thought about only if it exists.

which is also equivalent by contraposition to:

5) Anything that does not exist, cannot be thought about.

Identity and Parmenides

The ship of Theseus is a good example of the problem of identity. Plutarch wrote about Theseus' ship which would be repaired plank by plank while out at sea. Philosophers have thought about this problem in relation to the ship: at what point is the ship no longer the same ship? The Mereologicaly Theory of Identity (MTI) states that the identity of the ship is located in the identity of its parts, such that X = Y if and only if all the part of X are also the same parts in Y. The advantage of MTI is in that it is very easy to draw the line of identity. The problem, however, is that we no longer can call identical many things that we believe persist through chance, including ourselves. If we deny MTI, however, then we must determine where the line is during change that transforms one thing into another.

Parmenides was concerned about such problems. His criticism of Heraclitus, and the paradoxes that Heraclitus seemed to introduce, was that if we take our observations about the world seriously, then we cannot help getting into logical trouble. Parmenides, therefore, determined to solve the problem of the one and the many (being and becoming) by ignoring the sensible world and arguing purely from reason, a priori. His became a deductive argument that all things are one and that change is an illusion.